Electric-field-induced optical second-harmonic generation and nonlinear optical rectification in semiconducting carbon nanotubes

We have calculated the nonlinear susceptibility for the optical second-harmonic generation (SHG) from a bundle of aligned single-walled carbon nanotubes (SWCNs) of the 'zig-zag' type subjected to a constant electric field Eo, parallel to their axis. The breakdown of inversion symmetry caused by the electric field is accompanied by the occurrence of the parity-forbidden two-photon transitions between the valence- and conduction-band edges. As a result, the third-order nonlinear-susceptibiliry chi((3)) spectrum for SHG clearly demonstrates two peaks strongly distinguished on intensity: one is the two-photon resonance exactly at the pump photon energy (h) over bar omega equal to one half of the band gap Delta(g); the other - small peak - sits at (h) over bar omega = Delta(g), which corresponds to the one-photon interband transitions. It is found that the intensity of both peaks grows sharply with an increase of the SWCN radius. The susceptibility chi(3) relevant to the effect of nonlinear optical rectification in SWCNs has also been calculated. It is shown that near the fundamental absorption edge, the electric voltage appearing on the ends of SWCNs due to the optical rectification effect sharply changes its polarity. For a bundle of identical (25,0) SWCNs, 3 mu m in length and placed in an electric field E-0 similar to 10(4) V cm(-1), the optical rectification voltage is found to be about 0.35 mu V under excitation of the sample by a continuous laser with a radiation intensity of 30 mW cm(-2), which may be of practical importance for mid-IR signal processing. (C) 2000 Elsevier Science B.V. All rights reserved.